Details

sample95.0ms

Algorithm

intervals

Results

32.0ms	46×	body	1280	valid
19.0ms	49×	body	640	valid
11.0ms	149×	body	80	valid
7.0ms	27×	body	320	valid
4.0ms	87×	body	80	nan
2.0ms	12×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	150	9
5	501	9
6	2070	9
done	5000	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
10.1b	(log (/ x (+ x y)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

261×	`times-frac`
221×	`*-un-lft-identity`
198×	`log-prod`
149×	`add-sqr-sqrt`
147×	`add-cube-cbrt`
144×	`exp-sum`
90×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-/l*`
37×	`distribute-lft-out`
24×	`associate-/r/`
13×	`div-inv`
12×	`add-exp-log` `flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `rem-log-exp` `clear-num` `log-pow`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 296

Calls

4 calls:

72.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
18.0ms	(/ x (+ x y))
21.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
53.0ms	(/ x (+ x y))
107.0ms	(* x (log (/ x (+ x y))))
62.0ms	(log (/ x (+ x y)))

simplify2.7s

Counts

308 → 308

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	478	5632
1	907	5087
2	3247	4597
done	5001	4594

prune999.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.4b	(log (/ (cbrt x) (cbrt (+ x y))))
4.1b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `rem-log-exp` `flip-+`
6×	`pow1` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `associate-r/` `associate-l/` `log-pow` `div-inv`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
29.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt x)
299.0ms	(cbrt x)
123.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
125.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify733.0ms

Counts

128 → 128

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	235	1894
1	475	1786
2	1208	1597
done	5000	1512

prune752.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.4b	(log (/ (cbrt x) (cbrt (+ x y))))
3.4b	(log (/ (cbrt x) (cbrt (+ x y))))
3.4b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

144×	`log-prod`
138×	`cbrt-prod`
126×	`times-frac`
122×	`*-un-lft-identity`
86×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`distribute-lft-out`
13×	`add-exp-log`
7×	`pow1`
6×	`cbrt-div` `rem-log-exp` `associate-/r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 196

Calls

4 calls:

2.0ms	(cbrt x)
17.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
16.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
10.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt x)
116.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
126.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
102.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.9s

Counts

208 → 208

Iterations

Useful iterations: 3 (949.0ms)

Iter	Nodes	Cost
0	177	3317
1	326	3085
2	793	2968
3	3118	2863
done	5002	2863

prune952.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

13.0ms

(/ (exp (- y)) x)

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ (exp (- y)) x)

simplify2.6s

Counts

34 → 34

Iterations

Useful iterations: 3 (612.0ms)

Iter	Nodes	Cost
0	66	311
1	128	300
2	473	282
3	3443	278
done	5001	278

prune87.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes73.0ms

Accuracy

97% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 5.3b

bsearch196.0ms

Steps

Iters	Range		Point
9	0.004463962237743991	1051.5641664341613	2.134762495789531
8	-3.667948724445863e+96	-2.39912100600768e+92	-2.575795415940148e+92

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	49
1	27	45
done	27	45

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1516×	body	1280	valid
728.0ms	1445×	body	640	valid
488.0ms	4875×	body	80	valid
277.0ms	809×	body	320	valid
215.0ms	2956×	body	80	nan
74.0ms	436×	body	160	valid